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%I #14 May 25 2022 11:49:25
%S 1,1,2,2,3,4,5,6,7,10,10,13,16,18,21,24,31,31,38,44,49,56,62,76,76,90,
%T 100,113,126,136,161,161,186,201,234,252,267,308,308,349,370,449,462,
%U 483,546,546,609,637,813,792
%N Number of partitions of n into parts that are distinct mod 7.
%H Fausto A. C. Cariboni, <a href="/A114095/b114095.txt">Table of n, a(n) for n = 1..1000</a>
%e a(7)=5 because there are 5 such partitions of 7: {7}, {1,6}, {2,5}, {3,4}, {4,2,1}.
%t << DiscreteMath`Combinatorica`; np[n_]:= Length@Select[Mod[ #,7]& /@ Partitions[n],(Length@# == Length@Union@#)&]; lst = Array[np,50] (* corrected by _Seth A. Troisi_, May 17 2022 *)
%o (PARI) a(n) = my(nb=0); forpart(p=n, if (#p == #Set(apply(x->(x%7), Vec(p))), nb++)); nb; \\ _Michel Marcus_, May 18 2022
%K nonn
%O 1,3
%A _Giovanni Resta_, Feb 06 2006
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